Table A2 Carhart asset pricing model GPR...

Table A2

Carhart asset pricing model GPR / EPU

Carhart APM and geopolitical risk: January 1994–December 2023
	$J_{T_{1}}$	$J_{T_{2}}$	$J_{T_{3}}$	$J_{T_{4}}$	$J_{T_{5}}$	$J_{T_{6}}$	$J_{T_{7}}$	$J_{T_{8}}$	$J_{T_{9}}$	$J_{T_{10}}$
	4.61	3.52	4.66	1.89	1.85	3.88	3.55	4.76	4.11	5.32
	(0.46)	(0.62)	(0.46)	(0.87)	(0.87)	(0.57)	(0.62)	(0.45)	(0.53)	(0.38)
	α₁	α₂	α₃	α₄	α₅	α₆	α₇	α₈	α₉	α₁₀
	0.202	−0.031	0.310	0.541	−0.053	−0.047	0.241	0.305	0.176	−0.100
	(0.75)	(0.12)	(1.22)	(1.40)	(0.19)	(0.17)	(0.61)	(1.18)	(0.58)	(0.34)
	β_k,1	β_k,2	β_k,3	β_k,4	β_k,5	β_k,6	β_k,7	β_k,8	β_k,9	β_k,10
MKT	0.774	0.765	0.681	0.833	1.002	0.930	1.050	0.699	0.888	1.071
MKT	(7.47)	(7.68)	(8.87)	(2.56)	(7.86)	(5.71)	(5.38)	(6.80)	(5.46)	(6.05)
SMB	0.215	0.562	0.203	0.166	0.843	0.298	0.719	0.199	0.486	0.425
SMB	(2.97)	(7.13)	(2.38)	(1.30)	(6.63)	(2.81)	(4.97)	(2.80)	(4.43)	(4.44)
HML	0.593	0.856	0.585	0.275	0.922	0.640	0.964	0.553	0.771	0.872
HML	(5.77)	(5.99)	(3.61)	(0.94)	(7.17)	(4.80)	(3.73)	(5.23)	(3.90)	(4.72)
UMD	−0.013	−0.343	−0.163	−0.255	−0.821	−0.116	−0.493	−0.028	−0.376	−0.312
UMD	(0.13)	(2.38)	(3.60)	(1.49)	(3.94)	(0.79)	(2.60)	(0.29)	(2.35)	(2.16)
GPR	0.028	0.017	0.020	0.032	0.027	0.036	0.042	0.026	0.036	0.040
GPR	(4.38)	(3.28)	(3.90)	(3.18)	(3.99)	(5.04)	(6.61)	(4.31)	(6.47)	(6.26)

Carhart APM and geopolitical risk: January 1994–December 2023
	$J_{T_{1}}$	$J_{T_{2}}$	$J_{T_{3}}$	$J_{T_{4}}$	$J_{T_{5}}$	$J_{T_{6}}$	$J_{T_{7}}$	$J_{T_{8}}$	$J_{T_{9}}$	$J_{T_{10}}$
	4.61	3.52	4.66	1.89	1.85	3.88	3.55	4.76	4.11	5.32
	(0.46)	(0.62)	(0.46)	(0.87)	(0.87)	(0.57)	(0.62)	(0.45)	(0.53)	(0.38)
	α₁	α₂	α₃	α₄	α₅	α₆	α₇	α₈	α₉	α₁₀
	0.202	−0.031	0.310	0.541	−0.053	−0.047	0.241	0.305	0.176	−0.100
	(0.75)	(0.12)	(1.22)	(1.40)	(0.19)	(0.17)	(0.61)	(1.18)	(0.58)	(0.34)
	β_k,1	β_k,2	β_k,3	β_k,4	β_k,5	β_k,6	β_k,7	β_k,8	β_k,9	β_k,10
MKT	0.774	0.765	0.681	0.833	1.002	0.930	1.050	0.699	0.888	1.071
MKT	(7.47)	(7.68)	(8.87)	(2.56)	(7.86)	(5.71)	(5.38)	(6.80)	(5.46)	(6.05)
SMB	0.215	0.562	0.203	0.166	0.843	0.298	0.719	0.199	0.486	0.425
SMB	(2.97)	(7.13)	(2.38)	(1.30)	(6.63)	(2.81)	(4.97)	(2.80)	(4.43)	(4.44)
HML	0.593	0.856	0.585	0.275	0.922	0.640	0.964	0.553	0.771	0.872
HML	(5.77)	(5.99)	(3.61)	(0.94)	(7.17)	(4.80)	(3.73)	(5.23)	(3.90)	(4.72)
UMD	−0.013	−0.343	−0.163	−0.255	−0.821	−0.116	−0.493	−0.028	−0.376	−0.312
UMD	(0.13)	(2.38)	(3.60)	(1.49)	(3.94)	(0.79)	(2.60)	(0.29)	(2.35)	(2.16)
GPR	0.028	0.017	0.020	0.032	0.027	0.036	0.042	0.026	0.036	0.040
GPR	(4.38)	(3.28)	(3.90)	(3.18)	(3.99)	(5.04)	(6.61)	(4.31)	(6.47)	(6.26)

Carhart APM and Political Uncertainty: January 1994 to December 2023
	$J_{T_{1}}$	$J_{T_{2}}$	$J_{T_{3}}$	$J_{T_{4}}$	$J_{T_{5}}$	$J_{T_{6}}$	$J_{T_{7}}$	$J_{T_{8}}$	$J_{T_{9}}$	$J_{T_{10}}$
	5.53	3.81	7.08	2.45	2.03	4.84	6.18	6.16	5.99	5.68
	(0.35)	(0.58)	(0.22)	(0.78)	(0.85)	(0.44)	(0.29)	(0.29)	(0.31)	(0.34)
	α₁	α₂	α₃	α₄	α₅	α₆	α₇	α₈	α₉	α₁₀
	0.224	−0.024	0.332	0.583	−0.060	−0.019	0.420	0.320	0.274	−0.033
	(0.84)	(0.10)	(1.33)	(1.54)	(0.21)	(0.07)	(1.09)	(1.24)	(0.91)	(0.11)
	β_k,1	β_k,2	β_k,3	β_k,4	β_k,5	β_k,6	β_k,7	β_k,8	β_k,9	β_k,10
MKT	0.791	0.774	0.702	0.803	0.989	0.963	0.991	0.728	0.857	1.017
MKT	(8.20)	(7.81)	(8.95)	(2.46)	(7.83)	(6.38)	(5.11)	(7.28)	(5.24)	(5.90)
SMB	0.264	0.578	0.253	0.200	0.850	0.325	0.726	0.246	0.485	0.436
SMB	(3.51)	(6.88)	(2.65)	(1.56)	(6.79)	(3.20)	(4.60)	(3.28)	(4.16)	(4.26)
HML	0.650	0.859	0.582	0.285	0.954	0.718	0.884	0.595	0.704	0.807
HML	(5.76)	(5.89)	(3.12)	(1.07)	(7.45)	(5.70)	(3.34)	(5.22)	(3.60)	(4.42)
UMD	−0.038	−0.343	−0.198	−0.296	−0.842	−0.127	−0.574	−0.053	−0.426	−0.365
UMD	(0.39)	(2.34)	(3.92)	(1.77)	(4.19)	(0.91)	(2.95)	(0.55)	(2.60)	(2.46)
EPU1	0.055	0.043	0.109	0.051	−0.003	0.050	0.058	0.054	0.062	0.063
EPU1	(2.32)	(1.74)	(3.25)	(2.03)	(0.10)	(2.04)	(1.86)	(2.31)	(2.28)	(2.27)

Carhart APM and Political Uncertainty: January 1994 to December 2023
	$J_{T_{1}}$	$J_{T_{2}}$	$J_{T_{3}}$	$J_{T_{4}}$	$J_{T_{5}}$	$J_{T_{6}}$	$J_{T_{7}}$	$J_{T_{8}}$	$J_{T_{9}}$	$J_{T_{10}}$
	5.53	3.81	7.08	2.45	2.03	4.84	6.18	6.16	5.99	5.68
	(0.35)	(0.58)	(0.22)	(0.78)	(0.85)	(0.44)	(0.29)	(0.29)	(0.31)	(0.34)
	α₁	α₂	α₃	α₄	α₅	α₆	α₇	α₈	α₉	α₁₀
	0.224	−0.024	0.332	0.583	−0.060	−0.019	0.420	0.320	0.274	−0.033
	(0.84)	(0.10)	(1.33)	(1.54)	(0.21)	(0.07)	(1.09)	(1.24)	(0.91)	(0.11)
	β_k,1	β_k,2	β_k,3	β_k,4	β_k,5	β_k,6	β_k,7	β_k,8	β_k,9	β_k,10
MKT	0.791	0.774	0.702	0.803	0.989	0.963	0.991	0.728	0.857	1.017
MKT	(8.20)	(7.81)	(8.95)	(2.46)	(7.83)	(6.38)	(5.11)	(7.28)	(5.24)	(5.90)
SMB	0.264	0.578	0.253	0.200	0.850	0.325	0.726	0.246	0.485	0.436
SMB	(3.51)	(6.88)	(2.65)	(1.56)	(6.79)	(3.20)	(4.60)	(3.28)	(4.16)	(4.26)
HML	0.650	0.859	0.582	0.285	0.954	0.718	0.884	0.595	0.704	0.807
HML	(5.76)	(5.89)	(3.12)	(1.07)	(7.45)	(5.70)	(3.34)	(5.22)	(3.60)	(4.42)
UMD	−0.038	−0.343	−0.198	−0.296	−0.842	−0.127	−0.574	−0.053	−0.426	−0.365
UMD	(0.39)	(2.34)	(3.92)	(1.77)	(4.19)	(0.91)	(2.95)	(0.55)	(2.60)	(2.46)
EPU1	0.055	0.043	0.109	0.051	−0.003	0.050	0.058	0.054	0.062	0.063
EPU1	(2.32)	(1.74)	(3.25)	(2.03)	(0.10)	(2.04)	(1.86)	(2.31)	(2.28)	(2.27)

Note(s): This table reports the average pricing errors (α_i), coefficients of β_k,i and goodness-of-fit statistics obtained from the GMM estimation of system (1) using monthly data from January 1994 to December 2023. We use the FTSE Nareit U.S. REIT indices for 10 real estate sectors. p1: Apartment; p2: Diversified; p3: Healthcare; p4: Industrial; p5: Lodging Resorts; p6: Office; p7: Regional Malls; p8: Residential; p9: Retail; p10: Shopping Centers. J_T is Hansen’s statistic (to test the model’s over-identifying restrictions) and p-values are provided in parentheses

The model is the five-factor APM. The factors are the market excess return (MKT), SMB and HML the Fama and French size (small minus big) and book-to-market (high minus low) factors, the momentum factor, UMD (up minus down) introduced by Carhart, the geopolitical risk index (GPR), introduced by Caldara and Iacoviello (2022) and the economic policy uncertainty indices (EPU1, EPU2), introduced by Baker et al. (2016). EPU1 is the “Three Components Index”. EPU2 is the “News Based Policy Uncertainty Index”. For the estimates (α and β) the t-stats are provided in parentheses. The table reports the results of the augmented Fama and French asset pricing models, adding the GPR index or the EPU1 index. N.B. critical values for t-stats are 1.645 (at 10%), 1.960 (at 5%), 2.576 (at 1%)

Source(s): Table created by authors

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